Vol. 10, No. 1, 2021

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Exact modularity of line graphs of complete graphs

Mikhail Ipatov

Vol. 10 (2021), No. 1, 61–75

Modularity is designed to measure the strength of a division of a network into clusters. For n , consider a set S of n elements. Let V be the set of all subsets of S of size r. Consider the graph G(n,r,s) with vertices V and edges that connect two vertices if and only if their intersection has size s. In this article, we find the exact modularity of G(n,2,1) for n 5.

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modularity, line graphs, Johnson graphs
Mathematical Subject Classification
Primary: 05C76
Received: 14 May 2020
Revised: 12 July 2020
Accepted: 27 July 2020
Published: 16 January 2021
Mikhail Ipatov
Mechanics and Mathematics Faculty
Moscow State University